Investigations on reproducing kernel particle method enriched by partition of unity and visibility criterion

This work introduces a numerical integration technique based on partition of unity (PU) to reproducing kernel particle method (RKPM) and presents an implementation of the visibility criterion for meshfree methods. According to the theory of PU and the inherent features of Gaussian quadrature, the convergence property of the PU integration is studied in the paper. Moreover, the practical approaches to implement the PU integration are presented in different strategies. And a method to carry out visibility criterion is presented to handle the problems with a complex domain. Furthermore, numerical examples have been performed on the h-version and p-like version convergence studies of the PU integration and the validity of visibility criterion. The results demonstrate that PU integration is a feasible and effective numerical integration technique, and RKPM enriched by PU integration and visibility criterion is of more efficiency, versatility and high performance.